{
  "id": "2312.12779",
  "version": "v1",
  "published": "2023-12-20T05:36:47.000Z",
  "updated": "2023-12-20T05:36:47.000Z",
  "title": "A distinction between the paraboloid and the sphere in weighted restriction",
  "authors": [
    "Alex Iosevich",
    "Ruixiang Zhang"
  ],
  "categories": [
    "math.CA",
    "math.CO",
    "math.NT"
  ],
  "abstract": "For several weights based on lattice point constructions in $\\mathbb{R}^d (d \\geq 2)$, we prove that the sharp $L^2$ weighted restriction inequality for the sphere is very different than the corresponding result for the paraboloid. The proof uses Poisson summation, linear algebra, and lattice counting. We conjecture that the $L^2$ weighted restriction is generally better for the circle for a wide variety of general sparse weights.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-20T05:36:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "paraboloid",
      "distinction",
      "lattice point constructions",
      "general sparse weights",
      "wide variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}